Finite Group Databasebeta

← #18004828

Subgroups — #18004828

Order 4736.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558156C211yesmaximal, characteristic
2#14558010C211yesmaximal, characteristic, complemented
3#14557857C211yesmaximal, characteristic
4#14557827C211yesmaximal, characteristic, complemented
5#14557817C211yesmaximal, characteristic, complemented
6#14557758C211yesmaximal, characteristic, complemented
7#14557758C211yesmaximal, characteristic, complemented
8#14557688C211yesmaximal, characteristic, complemented
9#14557674C211yesmaximal, characteristic
10#14557637C211yesmaximal, characteristic, complemented
11#14557632C211yesmaximal, characteristic, complemented
12#14557625C211yesmaximal, characteristic, complemented
13#14557620C211yesmaximal, characteristic, complemented
14#14557591C211yesmaximal, characteristic, complemented
15C37×#485C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C2×#10596942C2211yescharacteristic
18C2×#10596942C2211yescharacteristic
19C2×#10596930C2211yescharacteristic
20C2×#10596930C2211yescharacteristic
21#11924535C2211yescharacteristic
22#11924531—21no—
23#11924525C2211yescharacteristic
24#11924522—21no—
25#11924518—21no—
26#11924516—21no—
27#11924510C2211yescharacteristic
28Q8×Dic37C2211yescharacteristic
29C4×Dic74—21no—
30C4×Dic74—21no—
31#11924501C2211yescharacteristic
32#11924501C2211yescharacteristic
33#11924501C2211yescharacteristic
34#11924501C2211yescharacteristic
35#11924498C2211yescharacteristic
36#11924495C2211yescharacteristic
37#11924492—21no—
38#11924492—21no—
39#11924469C2211yescharacteristic
40#11924467C2211yescharacteristic
41#11924465C2211yescharacteristic
42#11924465C2211yescharacteristic
43#11924461C2211yescharacteristic
44#11924461C2211yescharacteristic
45#11924459C2211yescharacteristic
46#11924459C2211yescharacteristic
47#11924456C2211yescharacteristic
48#11924456C2211yescharacteristic
49C22⋊#64436C2211yescharacteristic
50#11924446C2211yescharacteristic
51C8×Dic37C2211yescharacteristic
52C22⋊Q8×C37C2211yescharacteristic
53#117×C37C2211yescharacteristic
54#107×C37C2211yescharacteristic
55#106×C37C2211yescharacteristic
56#103×C37C2211yescharacteristic
57#103×C37C2211yescharacteristic
58C22⋊C8×C37C2211yescharacteristic
59C2×Q8×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C2×C22⋊D37—21no—
62C22×Dic37—21no—
63C2×D148C2311yescharacteristic
64C2×C4×D37—21no—
65C2×Dic74—21no—
66C2×Dic74—22no—
67C2×Dic74—22no—
68C2×Dic74—21no—
69C2×Dic74C2311yescharacteristic
70C2×Dic74C2311yescharacteristic
71C2×C8×C37C2311yescharacteristic
72C2×C8×C37C2311yescharacteristic
73C4⋊C4×C37—21no—
74C4⋊C4×C37C2311yescharacteristic
75C4⋊C4×C37C2311yescharacteristic
76C4⋊C4×C37C2311yescharacteristic
77C22⋊C4×C37—21no—
78C22⋊C4×C37—21no—
79C42×C37—21no—
80C22⋊Dic37D411yescharacteristic
81C22⋊Dic37D411yescharacteristic
82#10596942—22no—
83#10596942—22no—
84#10596938—21no—
85#10596938—21no—
86#10596938—21no—
87#10596938—21no—
88C4⋊Dic37—21no—
89C4⋊Dic37D411yescharacteristic
90C4⋊Dic37D411yescharacteristic
91C4⋊Dic37C2311yescharacteristic
92#10596936—21no—
93#10596936—21no—
94#10596936—21no—
95#10596936—21no—
96#10596936—21no—
97C4×Dic37—21no—
98C4×Dic37—21no—
99C4×Dic37—21no—
100C4×Dic37—21no—
101C4×Dic37—21no—
102C4×Dic37C2311yescharacteristic
103C4×Dic37C2311yescharacteristic
104C2×#64436C2311yescharacteristic
105C2×#64436C2311yescharacteristic
106#10596930—22no—
107#10596930—22no—
108C23×C37C2×D411yescharacteristic
109C22×D37—21no—
110Q8×C37—21no—
111Q8×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37C2×D411yescharacteristic
119C2×C4×C37C2411yescharacteristic
120C22⋊D37—81no—
121C2×Dic37—24no—
122C2×Dic37—21no—
123C2×Dic37—21no—
124C2×Dic37—21no—
125C2×Dic37C2×D411yescharacteristic
126C2×Dic37C2×D411yescharacteristic
127C2×Dic37C2×D411yescharacteristic
128C2×Dic37C2×D411yescharacteristic
129D148—21no—
130D148—21no—
131C4×D37—81no—
132Dic74—24no—
133Dic74—21no—
134Dic74—21no—
135Dic74—81no—
136Dic74#4112yes—
137Dic74#4112yes—
138C8×C37—21no—
139C8×C37—21no—
140#64436—21no—
141#64436—21no—
142C22×C37—21no—
143C22×C37—21no—
144C22×C37—21no—
145C22×C37C22×D411yescharacteristic
146C2×D37—41no—
147C2×D37—41no—
148C2×D37—41no—
149C4×C37—21no—
150C4×C37—41no—
151C4×C37—41no—
152C4×C37—41no—
153C4×C37—41no—
154C4×C37C2×#4111yescharacteristic
155C4×C37C2×#4111yescharacteristic
156Dic37—22no—
157Dic37—22no—
158Dic37—21no—
159Dic37—21no—
160Dic37—21no—
161Dic37—21no—
162Dic37—41no—
163#3121—371nomaximal, Sylow
164C2×C37—41no—
165C2×C37#52511yescharacteristic
166C2×C37#57711yescharacteristic
167C2×C37#57811yescharacteristic
168D37—81no—
169#542—371no—
170#519—371no—
171#485D3711yescharacteristic, complemented
172#482—371no—
173#477—371no—
174#475—371no—
175#464—371no—
176#464—371no—
177#451—371no—
178#448—371no—
179#441—371no—
180#440—371no—
181C4×Q16—371no—
182C4×SD16—371no—
183#433—371no—
184C37#312111yescharacteristic, complemented, Sylow
185C22×Q8—371no—
186C2×Q16—371no—
187C2×Q16—371no—
188C2×SD16—371no—
189C2×SD16—371no—
190C4⋊Q8—371no—
191#126—741no—
192#124—371no—
193#124—741no—
194#123—741no—
195C22⋊Q8—741no—
196C22⋊Q8C2×D3711yescharacteristic
197#121—371no—
198C4×Q8—371no—
199C4×Q8—371no—
200C4×Q8—371no—
201C4×Q8—371no—
202C4×Q8—371no—
203C4×Q8—741no—
204C4×Q8—741no—
205C4×D4—371no—
206#117—371no—
207#117—741no—
208#117—741no—
209#117C2×D3711yescharacteristic
210#107—371no—
211#107C2×D3711yescharacteristic
212#106—371no—
213#106C2×D3711yescharacteristic
214C4⋊C8—371no—
215C4⋊C8—371no—
216#103—371no—
217#103—371no—
218#103—371no—
219#103—371no—
220#103C2×D3711yescharacteristic
221#103C2×D3711yescharacteristic
222#102—371no—
223#102—371no—
224C22⋊C8—371no—
225C22⋊C8C2×D3711yescharacteristic
226#97—371no—
227C4×C8—371no—
228C2×Q8—371no—
229C2×Q8—371no—
230C2×Q8—741no—
231C2×Q8—742no—
232C2×Q8—742no—
233C2×Q8—741no—
234C2×Q8C22×D3711yescharacteristic
235C2×D4—371no—
236C2×D4—741no—
237C22×C4—741no—
238C22×C4—741no—
239C22×C4C22×D3711yescharacteristic
240Q16—742no—
241Q16—742no—
242SD16—742no—
243SD16—742no—
244C2×C8—371no—
245C2×C8—371no—
246C2×C8C22×D3711yescharacteristic
247C2×C8C22×D3711yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—371no—
250C4⋊C4—371no—
251C4⋊C4—371no—
252C4⋊C4—741no—
253C4⋊C4—741no—
254C4⋊C4—741no—
255C4⋊C4—741no—
256C4⋊C4—741no—
257C4⋊C4—741no—
258C4⋊C4C22×D3711yescharacteristic
259C4⋊C4C22×D3711yescharacteristic
260C4⋊C4C22×D3711yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—371no—
264C22⋊C4—371no—
265C22⋊C4—741no—
266C22⋊C4—741no—
267C22⋊C4—741no—
268C22⋊C4—741no—
269C42—21no—
270C42—371no—
271C42—371no—
272C42—741no—
273C42—741no—
274C42—741no—
275C42—741no—
276C42—741no—
277C23—741no—
278C23D4×D3711yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—372no—
282Q8—372no—
283Q8—2961no—
284Q8—744no—
285Q8—741no—
286Q8—741no—
287D4—2961no—
288D4—741no—
289D4—741no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—371no—
297C2×C4—371no—
298C2×C4—371no—
299C2×C4—371no—
300C2×C4—2961no—
301C2×C4—744no—
302C2×C4—741no—
303C2×C4—741no—
304C2×C4—741no—
305C2×C4D4×D3711yescharacteristic
306C2×C4C23×D3711yescharacteristic
307C8—21no—
308C8—21no—
309C8—741no—
310C8—741no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—1481no—
315C22—1481no—
316C22—1481no—
317C22C2×D4×D3711yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—742no—
324C4—742no—
325C4—741no—
326C4—741no—
327C4—741no—
328C4—741no—
329C4—1481no—
330C4#41×D3711yescharacteristic
331C4#41×D3711yescharacteristic
332C2—41no—
333C2—2961no—
334C2#1455804111yescharacteristic
335C2#1455834011yescharacteristic
336C2#1455834911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#485C2
socleC22×C37C22×D4
prime radical#11924510C22
hypercenter#485D37
hypocenterC37#3121
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14558010C2semidirect
4. #14557827C2semidirect
5. #14557817C2semidirect
6. #14557758C2semidirect
7. #14557758C2semidirect
8. #14557688C2semidirect
10. #14557637C2semidirect
11. #14557632C2semidirect
12. #14557625C2semidirect
13. #14557620C2semidirect
14. #14557591C2semidirect
15. C37×#485C2semidirect
171. #485D37semidirect
184. C37#3121semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145581562
#145580102
#145578572
#145578272
#145578172
#145577582
#145576882
#145576742
#145576372
#145576322
#145576252
#145576202
#145575912
C37×#4852
#312137